In the production of semiconductor devices, small contact elements on the semiconductor chip have to be connected to electrical terminals which provide a contact to the outside world. These connections are generally realized as part of the package or encapsulation of the semiconductor chip, e.g. by providing a metallization layer on a face of the chip which provides conducting elements or lines connecting the contact elements of the chip to contact elements on an outer face of the package, e.g. solder balls. Especially with high pin counts, the problem frequently occurs that the high number of conducting lines in the layer cannot be arranged without crossings between at least some of the lines. In a single metallization layer, a crossing of two lines can not be realized because this would cause an electrical shortcut between the lines. Hence, in this case a second metallization layer has to be provided in order to arrange the connections between the chip and the contact elements to the outside.